[rmorey]

I remember in high school precalc, we learned about the Taylor series, and my teacher told us that it was how trig functions were actually implemented on calculators. Well I looked it up and found that it was actually CORDIC, and went and had some fun implementing it in TI Basic

[djmips]

I thought you might be interested to read how the remarkable Sinclair scientific calculator did it's trig, log etc. It wasn't Cordic but the algorithm has similarities.

http://files.righto.com/calculator/sinclair_scientific_simul...

[rossant]

Well, are there _any_ calculators out there that use Taylor expansions?

[snovv_crash]

I've done some work with fast approximate math libraries,and went down this path. Taylor was a dead-end, but Chebyshev polynomials work great. They have the nice property of having (close to) the minimum maximum (minimax) error over the entire range you are approximating.

[toolslive]

well, from memory (this was > 20y ago)

  - Taylor gives you polynomial optimized for the evaluation of one point.
  - naive Newton gives you a polynomial with 0 error in the interpolation points [but the system has a bad condition]
  - Chebychev gives you a polynomial with minimal error over the interval of choice.

So there is no real reason to ever use the Taylor series to approximate a function over an interval. The high school math teachers are lying.

[rmorey]

not lying, probably just mistaken